High-density sensing of biopotentials is gaining increasing interest in bio-imaging applications as well as in other applications such as health monitoring and neuroprostheses. However, these devices are severely energy constrained because of the energy required to sense and communicate high-resolution signals, as well as limitations on energy dissipated near the tissue. The energy and area constraints are ultimately what limit the maximum density (and number) of these devices.
It has been observed that spatially dense biopotentials tend to also be highly correlated. This is for multiple reasons, such as:                Distance from the source of potentials, for example in Electroencephalography (EEG), where 1-1.5 cm separate the brain from the scalp, acts as a low-pass spatial filter to electromagnetic waves, thereby reducing the content of high-spatial-frequency signals, and introducing high spatial correlations.        The underlying biological sources of electromagnetic (EM) waves often travel along contiguous paths, and exist over non-negligible volumes, thereby introducing spatial correlations even at the source level.        Sources of noise are often other biopotential sources themselves that are again spatially correlated.        Electrodes themselves act as spatial low-pass filters by spatially averaging electric potential around them.        
Even with the highly correlated data, high-density sensing is required to gather important information buried even in the “less significant” bits of each observation. Because of decay of high spatial frequencies, as illustrated in FIG. 1, these lower order bits are the ones carrying high-resolution information. Perhaps as an acknowledgement of this fact, many state-of-the-art systems record each electrode at a very high precision, for example 24-bit analog-to-digital converters (ADCs), with 256 or more sensors. Small differences between recordings of nearby sensors matter, likely because these differences capture events that generate small variations in potential either due to their shallow depth or small spatial extent.
There are two commonly used topologies for biopotential electrode referencing. In the first topology, shown in FIG. 2, all electrodes are referenced directly against a global reference (sometimes called “unipolar” or “direct global referencing”). The corresponding tree has one root node with all other nodes as its children. This topology requires that all electrode ADCs be of very high precision in order to detect the small informative differences between each electrode.
FIG. 3 shows the second topology, sometimes called “sequential bipolar referencing,” where each electrode is referenced to an electrode prior to it in a chain of electrodes leading to a tree where each node has one child. There are two problems with this simplistic electrode-chain strategy. In many applications, especially those pertaining to source localization and imaging, algorithms commonly use signals referenced against a global reference where potential is recovered with respect to a single global reference. While it may seem that adding the differentially sensed potentials appropriately would yield signal with respect to the global reference, that is incorrect due to errors also adding up, and quantization noises and errors introduced by the circuit components (such as the amplifier and the ADC) of the electrodes also add as the signals are added resulting in large overall noise. Further, it is necessary to verify almost all electrodes for good contact, for if one electrode in the chain has poor contact, then the recordings of all ensuing electrodes will be unusable.